Is it possible to select multiple types of issues when creating an issue

[Nic Brough -Adaptavist-]

The issue type is a defining property of an issue, it makes no sense to have something that is a "bug" and an "improvement" at the same time, it's one or the other.

So, no.  You can only give an issue one type.

You can have many types in a project of course, just check the "issue type scheme" for it.